/* Routines for standard interval arithmetic    */

/****************************************************************************/
/* (C) Copyright 1993 Universidade Estadual de Campinas (UNICAMP)           */
/*                    Campinas, SP, Brazil                                  */
/*                                                                          */
/* This file can be freely distributed, modified, and used for any          */
/*   non-commercial purpose, provided that this copyright and authorship    */
/*   notice be included in any copy or derived version of this file.        */
/*                                                                          */
/* DISCLAIMER: This software is offered ``as is'', without any guarantee    */
/*   as to fitness for any particular purpose.  Neither the copyright       */
/*   holder nor the authors or their employers can be held responsible for  */
/*   any damages that may result from its use.                              */
/****************************************************************************/

#ifndef IA_H
#define IA_H

#include <flt.h>
#include <stdio.h>
#include <math.h>

typedef struct {Float lo, hi; } Interval;

void ia_init (void);
  /* Initializes the constants (ia_full, etc.) */
  /* MUST be called at least once before any of the routines below. */

Interval ia_full (void); /* The "anything" interval, [-Inf .. +Inf] */

int ia_is_full (Interval *x); 
  /* True iff $*x.lo$ is -Inf or $*x.hi$ is +Inf */
  
void ia_norm_full (Interval *x);
  /* If $*x.lo$ is -Inf or $*x.hi$ is +Inf, sets $*x$ to [-Inf .. +Inf] */

Interval ia_const (Float x, Float err); /* $x$ plus or minus $err$ */

Interval ia_int_const (int i);  /* $i$, with rounding error if too big. */

Interval ia_add   (Interval x, Interval y);
Interval ia_sub   (Interval x, Interval y);
Interval ia_neg   (Interval x);
Interval ia_scale (Interval x, Float alpha, Float zeta); /* $\alpha x / \zeta$ */
Interval ia_shift (Interval x, Float gamma);  /* $x + \gamma$ */
Interval ia_mul   (Interval x, Interval y);
Interval ia_div   (Interval x, Interval y);
Interval ia_sqr   (Interval x); /* same as ia_mul(x,x), only better */
Interval ia_inv   (Interval x);
Interval ia_sqrt  (Interval x);
Interval ia_abs   (Interval x);
Interval ia_max   (Interval x, Interval y);
Interval ia_min   (Interval x, Interval y);

Interval ia_affine (
    Interval x, Float alpha, 
    Float zeta,
    Float gamma, Float delta
  );
  /* 
    Computes $\alpha x / \zeta + \gamma \pm \delta. */

Interval ia_affine_2(
    Interval x, Float alpha,
    Interval y, Float beta, 
    Float zeta, 
    Float gamma, Float delta
  );
  /* 
    Computes $(\alpha x + \beta y)/ \zeta + \gamma \pm \delta. */

/*** MISCELLANEOUS TOOLS ***/

Interval ia_meet (Interval x, Interval y);
  /* 
    Intersection of $x$ and $y$; error if disjoint. */

Interval ia_join (Interval x, Interval y);
  /* 
    Smallest interval contining $x$ and $y$. */

Interval ia_throw (void);
  /* 
    Returns a random interval, suitable for testing.
    The client must have called $srandom(<seed>)$. */

void ia_print (FILE *f, Interval x);
  /* 
    Prints $x$ on $f$. */
    
#endif